A bstract Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in dispersion relation and full crossing symmetry of scattering amplitude, we derive several sets generically nonlinear positivity for a generic scalar theory: refer these as P Q , D su stu $$ {\overline{D}}^{\mathrm{stu}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/Ma...

A bstract We present positivity bounds, derived from the principles of analyticity, unitarity and crossing symmetry, that constrain low-energy constants chiral perturbation theory. Bounds are produced for 2, 3 or more flavours in meson-meson scattering with equal meson masses, up to including next-to-next-to-leading order (NNLO), using second higher derivatives amplitude. enhance bounds by most...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on allowed values Wilson coefficients. In this paper, we consider that arise from requirement low-energy causality alone, without appealing to any assumptions about UV physics. We focus shift-symmetric theories, propagation around both...

Positivity bounds - constraints on any low-energy effective field theory imposed by the fundamental axioms of unitarity, causality and locality in UV have recently been used to constrain various theories relevant for cosmology. However, date most these assumed that there is a single Lorentz-invariant vacuum which all fields zero expectation value many cosmologically models this not case. We exp...

We give elementary proofs of the fact that the Loewner matrices [ f(pi)−f(pj) pi−pj ] corresponding to the function f(t) = t on (0,∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0,∞) the Loewner matrices corresponding to an operator convex function on...

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

The presented work of this paper addresses the two shape properties, positivity and monotonicity of irregular surface data. The data is initially triangulated and a side-vertex scheme is adopted to interpolate the data over each triangle. Each boundary and radial curve is a rational function with three parameters facilitating 18 parameters in each triangular patch. The presence of these paramet...